Journal of Applied Computing and Information Technology ISSN 2230-4398, Volume 18, Issue 2, 2014 Incorporating the NACCQ publications: Bulletin of Applied Computing and Information Technology, ISSN 1176-4120 Journal of Applied Computing and Information Technology, ISSN 1174-0175 Refereed Article A2:
An evaluation of different delivery methods for teaching binary, hex and decimal conversion Daniel Kempthorne UCOL, New Zealand
[email protected] Dr. Aaron Steele UCOL, New Zealand
[email protected] Kempthorne, D. & Steele, A. (2014). An evaluation of different delivery methods for teaching binary, hex and decimal conversion. Journal of Applied Computing and Information Technology, 18(2). Retrieved June 2, 2015 from http://www.citrenz.ac.nz/jacit/JACIT1802/2014Kempthorne_NumberConversion.html Abstract The ability to convert between binary, hexadecimal, and decimal numbering systems is a fundamental skill commonly taught to tertiary-level computing and ICT students. This paper presents the results of a multiple year investigation into the application of differing approaches for the teaching and learning of these skills. Specifically, the study compares traditional lectures, games, and group activities with student levels of academic achievement. Student prior experience with numbering system conversion is also analysed. The study reveals that, overall, the game-based approach resulted in the highest average test scores; however, when students were divided into groups with and without prior experience, the students with prior experience performed better with a traditional lecture approach. Keywords computing education, binary, hexadecimal, decimal, conversion 1. Introduction Binary, hexadecimal, and decimal numbering systems are widely used and encountered within the field of computing and information and communications technology (Bryan & O'Hallaron, 2002). The binary and hexadecimal numbering systems are essential for understanding the fundamentals of how digital data is stored and manipulated within computing systems (Morley & Parker, 2012). Hexadecimal RGB colour codes are also used extensively within software and web development languages and environments (DiMarco, 2011). Consequently, understanding these numbering systems and possessing the ability to convert between these systems is an essential skill for ICT and computing students. At a tertiary level the decimal numbering system is already familiar to most students and does not need to be taught. However, converting back and forth between decimal and binary, decimal and hexadecimal, and binary and hexadecimal are skills requiring
intentional teaching and learning and are often covered in first year degree information systems and computer science curriculums. In the wider field of tertiary education, numerous techniques have been suggested as effective approaches for teaching and learning (Race, 2013). This study specifically focuses on three different approaches: traditional lecturing, group activities, and games: all of which have been studied with relation to various topics (Cendan, Silver, & Ben-David, 2011; DeNeve & Heppner, 1997; Ebner & Holzinger, 2007; Mayo, 2007; Savoy, Proctor, & Salvendy, 2009). However, little work has been done specifically focused on their effectiveness in teaching numbering system conversion and understanding. The traditional lecture approach examined in this study consisted of a lecturerfocused class where students were taught how to convert between the three numbering systems by the lecturer who was positioned at the front of the class. The group activities approach involved the lecturer giving a brief overview and then letting the students work together in groups. The game-based approach again involved the lecturer giving a brief overview of the basics at the front of the class before directing the students to use two different interactive games to practise conversion between the numbering systems. Ultimately the aim of this study was to discover whether a relationship existed between any of the aforementioned approaches to teaching number conversion and student levels of academic achievement and also student self-perceived confidence levels. 2. Method The research sample for this study consisted of 66 students enrolled in a Computer Fundamentals paper from the first year of a three year ICT degree. Data was collected over two semesters from eight different groups of students. In order to investigate whether a relationship existed between the different teaching and learning approaches, levels of academic achievement, and student self-perceived levels of confidence, the research sample was divided into three groups. Each group engaged with one of the three teaching and learning approaches (traditional lecture, group activity, and game-based). Students were then given the same formative assessment on binary, hexadecimal, and decimal number system conversion. Students were also asked prior to the lesson whether they had any experience converting between and/or using the different numbering systems; this would then be used to identify those students who has already been taught how to convert between numbering systems in a different paper on the degree. Finally, students were also asked to answer a four point Likert scale question relating to their confidence levels both before and after the lesson. Students who were extremely confident in their ability to convert between the number systems would circle 'Confident', whereas students who were not very confident would circle 'Not confident'. The purpose of this question was to gauge how the lesson had affected the confidence levels of the students according to the method they used to prepare for the assessment. The three different teaching methods were employed as follows: Method 1 - The traditional lecture method The traditional lecture approach consisted of the lecturer standing at the front of the class giving a traditional-style lecture, teaching the students how to convert between the three numbering systems. During this lecture a white board was used to help demonstrate examples and the students were able to ask questions freely. The lecture took approximately 30 minutes, after which the students were asked to complete a formative assessment. After the lecture but prior to the test the students were also asked for their self-perceived confidence levels with regard to converting between the numbering systems; the students were again asked to gauge their confidence on the same scale (Not Confident, Slightly Confident, Mostly Confident, or Confident) after completing the test. Of the 66 members of the research sample, 26 participated in the traditional lecture approach, 13 with prior experience and 13 without.
Method 2 - The group method The group activities approach involved the lecturer giving a brief five minute overview of the basics at the front of the class before letting the students work together in groups of 3-4 students to complete individual worksheets. Each group worked through a step-by-step paper-based guide, which outlined how to convert between the numbering systems. The group activities took approximately 25 minutes. At the conclusion of the group activity the students were asked to individually complete the formative assessment on the numbering systems. After the group activity but prior to the test, the students were asked for their self-perceived confidence levels with regard to converting between the numbering systems, this was also measured again after students completed the test. Of the 66 members of the research sample, 17 participated in the group activity approach, eight with prior experience and nine without. Method 3 - The game method The game approach involved the lecturer again giving a brief five minute overview of the basics at the front of the class before directing the students to individually use two different interactive games to practise the conversion of the numbering systems. The two games used consisted of the students being given the challenge of converting a number and they were given instant feedback as to whether they had responded correctly to the challenge. One game focused on converting between binary and decimal while the other game focused on converting between hexadecimal and binary. Students used the games for approximately 25 minutes before completing the formative assessment. After the game activity but prior to the test, the students were asked for their self-perceived confidence levels with regard to converting between the numbering systems, this was also measured again after students completed the test. Of the 66 members of the research sample, 23 participated in the educational game approach, 11 with prior experience and 12 without. After the students had completed the assessment they were able to see the correct answers and find out their results for the test. Furthermore, the students were then given the other two teaching methods for the remainder of the class to ensure that no student was disadvantaged by the first delivery method they were given at the beginning of the class. The results of the formative assessment were then analysed in conjunction with student confidence levels and grouped according to the three different teaching and learning approaches. The results of this analysis will be presented and discussed in the following sections. 3. Results Figure 1 presents the average mark (out of 30) for the entire research sample grouped according to teaching method. Figure 2 and Figure 3 show the average mark grouped according to teaching method for those with and for those without prior hexadecimal and binary conversion experience. It is interesting to note the slight differences between the three graphs, which will be discussed further in the following section.
Figure 1. Overall average results
Figure 2. Average result for students with prior binary/hex conversion experience
Figure 3. Average result for students without prior binary/hex conversion experience
The results suggest that overall, there is little difference between the three methods for teaching binary, hexadecimal, and decimal conversion. However, when students who have prior binary/hexadecimal conversion experience are isolated, the traditional lecturer approach (method 1) appears to be the most effective. Conversley, when the students without prior experience are isolated, the game-based approach appears to be the most effective with the traditional lecturer approach being the least effective. Figures 4, 5, and 6 present the student pre- and post- assessment confidence levels. The Likert scale values of Not Confident, Slightly Confident, Mostly Confident and Confident were given numerical values of 0, 1, 2, and 3 respectively for graphing purposes. The average test results are also displayed as a superimposed line on the secondary axis. Figure 4 shows the pre and post confidence levels for each teaching method for the entire class, while Figures 5 and 6 isolate the experience and inexperienced students.
Figure 4. Overall pre and post confidence levels with average results
Figure 5. Experienced students pre and post confidence levels with average results
Figure 6. Inexperienced students pre and post confidence levels with average results Interstingly, overall the traditional lecture approach (method 1) resulted in the highest pre-test confidence levels, however these students also had the lowest posttest confidence levels. In comparison, the group and game approaches resulted in lower pre-test confidence levels and much higher post-test confidence levels. This pattern can also be seen when the class is isolated into experience and inexperienced students, with the only variation being seen with inexperienced students, where the game approach resulted in the highest pre-test confidence levels. These results will be discussed in further detail in the following section. 4. Discussion It is worth noting that, overall, the average assessment grades are relatively similar across the three teaching methods, indicating that all three methods have their merits as valid approaches to teaching binary and hexadecimal conversion. However, perhaps the more interesting results begin to emerge when the class is divided into those students who had prior experience with the number systems and those who did not have such experience. When the students who have had prior experience working with the different numbering systems are viewed in isolation, it appears that the traditional lecture teaching method produces, on average, the highest test results (see Figure 2). This result could possibly be due to a number of different reasons, a few of which will now be discussed. For students with prior experience, the thirty minute lecture may have provided a reasonably thorough refresher on the topic. Students would likely have been able to relate the content of the lesson directly to previous experiences converting between the numbering systems, essentially having their existing knowledge reinforced and sharpened by the lecturer. Conversely, the group activity and game approaches provided less in-depth coverage of the topic from the lecturer and instead allowed students to participate in interactive learning experiences, either with each other or with a game. For students with prior experience, these activities required the students themselves to refresh their understanding of the topic. Accordingly, it is possible that the self-refreshment was less effective than the expert refreshment provided by the lecturer for these students. Interestingly, when the students who have not had prior experience converting between the numbering systems are isolated, a very different pattern can be seen. The traditional lecture approach, which emerged as the most effective method for students with prior experience, seems to be the least effective method for students without prior experience. Conversely, the group approach and game approach appeared more effective, with the game-based approach in particular appearing as the most effective for this particular group of students. Potentially, this difference between experienced and inexperienced students could be related to a key difference
in the teaching approaches. The traditional lecture provided students with thorough coverage of everything students needed to know about the topic. However, the traditional lecture did not involve students directly putting into practice the number system conversion techniques that were covered. The first time these students were required to convert between the number systems was during the assessment. In contrast, both the group activity and game approaches required the students to practically apply number conversion techniques in order to complete the respective activities. Accordingly, these students began the test having already practised the required number conversion techniques. Interestingly, when the students' self-perceived confidence levels are considered, a number of common themes begin to emerge. For each of the three teaching approaches an increase in confidence levels can be seen when pre and post levels are examined. This increase in confidence is also maintained when students with and without prior experience are analysed in isolation. This trend has likely little to do with the teaching approach and more to do with students' self-assessment of their own performance. For example, prior to the test students are unaware of how well they will perform and as a consequence may provide a more conservative confidence estimate. After the completion of the test, the students will likely have a clearer understanding of how well they felt they performed during the test, which could result in higher self-perceived confidence levels. A notable observation from the results is that the highest pre-test confidence levels were found among the students with prior experience who received the traditional lecture delivery method (see Figure 5). Correspondingly, these students also achieved the highest average test results. However, somewhat surprisingly, these students provided post-test confidence levels noticeably lower than the experienced students who were involved with the group and game approaches. Similarly, when the inexperienced students are isolated, the highest average pre-test confidence levels are found among the game approach students (see Figure 6). Again, considering only the inexperience students, this group (the game approach students) also achieved the highest average test results. It is interesting to note that, when the students are separated with regard to experience, the pre-test confidence level seems to emerge as an indicator of achievement. Thus the students who were more confident pre-test tended to have higher achievement. However, due to the size of the research sample, the researchers acknowledge that it would be unwise to generalise this finding. 5. Conclusion This paper set out to investigate the effectiveness of three different approaches for teaching binary, hexadecimal, and decimal number conversion. Based on the results, a traditional lecture approach emerged as the most effective for students who had previous experience in converting between the numbering systems. However, for students who lacked this experience, the traditional lecture approach was found to be the least effective, with inexperienced students showing greater understanding after having engaged with the game-based approach. The study also captured students' self-perceived levels of confidence pre and posttest. These findings indicate that students generally had lower pre-test confidence levels and higher post-test confidence levels. The study also found that students with prior experience who received the traditional lecture approach had the highest pretest confidence levels and also produced the highest average test results. The results also hinted that the pre-test confidence levels of students could be an indicator of achievement levels, however due to the limitations of the study (which will be addressed in the following section) the researchers felt it premature to assert this conclusion. Although this paper has presented some interesting findings, it is worth highlighting some of the limitations with regards to this study. The sample size of 66, although large enough to provide an initial insight, is still a relatively small sample size. Accordingly, the researchers are cautious of generalising the findings. The authors
believe that it would be worthwhile to see the study replicated with a larger research sample across different institutions and cultural environments to determine if the patterns identified within this study are universal. Nevertheless, this study has provided some interesting data relevant to educators tasked with teaching and assessing the numbering systems examined in this paper. Future work could include (as mentioned above) replicating the study with a larger research sample. In addition, more in-depth statistical analysis of the data could also be conducted once a larger research sample has been obtained. Analyses could also be conducted with other variables, for example, attitude toward subject and gender. Furthermore, qualitative data collection methods could also be employed to gain further insight into student perspectives of the three different teaching methods and student confidence levels. 6. References Bryant, R.E., & O'Hallaron, D. R. (2003). Computer systems: A programmer's perspective. Boston: Prentice Hall. Cendan, J. C., Silver, M., & Ben-David, K. (2011). Changing the student clerkship from traditional lectures to small group case-based sessions benefits the student and the faculty. Journal of Surgical Education, 68(2), 117-120. DeNeve, K. M., & Heppner, M. J. (1997). Role play simulations: The assessment of an active learning technique and comparisons with traditional lectures. Innovative Higher Education, 21(3), 231-246. DiMarco, J. (2011). Digital design for print and web: An introduction to theory, principles, and techniques. Hoboken, NJ: Wiley. Ebner, M., & Holzinger, A. (2007). Successful implementation of user-centered gamebased learning in higher education: An example from civil engineering. Computers & Education, 49(3), 873-890. Mayo, M. J. (2007). Games for science and engineering education. Communications of the ACM, 50(7), 30-35. Morley, D., & Parker, C. S. (2012). Understanding computers: Today and tomorrow. Boston: Cengage Learning. Race, P. (2013). The lecturer's toolkit: A practical guide to assessment, learning and teaching. Abingdon, UK: Routledge. Savoy, A., Proctor, R. W., & Salvendy, G. (2009). Information retention from PowerPoint™ and traditional lectures. Computers & Education, 52(4), 858-867. Copyright © 2014 Kempthorne, D. & Steele, A. Journal of Applied Computing and Information Technology (JACIT): ISSN 2230-4398 (Incorporating the Bulletin of Applied Computing and Information Technology, NACCQ: ISSN 1176-4120 and Journal of Applied Computing and Information Technology, NACCQ: ISSN 11740175) Copyright ©2014 CITRENZ. The author(s) assign to CITRENZ and educational non-profit institutions a nonexclusive licence to use this document for personal use and in courses of instruction provided that the article is used in full and this copyright statement is reproduced. The author(s) also grant a non-exclusive licence to CITRENZ to publish this document in full on the World Wide Web (prime sites and mirrors) and in printed form within the Journal of Applied Computing and Information Technology. Authors retain their individual intellectual property rights. Michael Verhaart, Donald Joyce and Nick Wallingford (Eds.). An Open Access Journal, DOAJ #22304398, ( ✓zotero)
